We calculate the thermodynamic functions of pure-glue QCD to three-loop orderusing the hard-thermal-loop perturbation theory (HTLpt) reorganization offinite temperature quantum field theory. We show that at three-loop orderhard-thermal-loop perturbation theory is compatible with lattice results forthe pressure, energy density, and entropy down to temperatures $T\simeq3\;T_c$.Our results suggest that HTLpt provides a systematic framework that can used tocalculate static and dynamic quantities for temperatures relevant at LHC.